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Progressive Meshes

Progressive Meshes. A Talk by Wallner and Wurzer for the overfull MathMeth auditorium. What it‘s all about. Overview. Advantages PM‘s Definition and Basics GeoMorphs Mesh Compression Selective Refinement Construction. Let‘s start off. Advantages of PM‘s. Mesh Simplification

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Progressive Meshes

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  1. Progressive Meshes A Talk by Wallner and Wurzer for the overfull MathMeth auditorium

  2. What it‘s all about...

  3. Overview • Advantages PM‘s • Definition and Basics • GeoMorphs • Mesh Compression • Selective Refinement • Construction

  4. Let‘s start off...

  5. Advantages of PM‘s • Mesh Simplification • LOD Approximation • Progressive Transmission • Mesh Compression • Selective Refinement

  6. Definition and Basics (1) • A corner is a (vertex,face) tuple • We are speaking of a sharp edge if • it is a boundary adge • the adjacent faces have different discrete values or • adjacent corners have different scalar values

  7. M0 Definition and Basics (2) • Traditional Mesh • Progressive Mesh (M0,{Vsplit0… Vsplitn-1}) K V

  8. Definition and Basics (3)  lossless ! vsplit vt vr vl vl vr vs ’ vs ecol

  9. ^ ^ M ... Full-Detailed Mesh (all vertices) M=Mn Definitions and Basics (4) M0 ... Minimal Detailed Version 13,546 500 152 150 M175 M1 M0 ecoln-1 ecol0 ecoli

  10. Geomorph • Smooth visual transition between two meshes Mf, Mc Mf Mc v1 v1 v2 v2 Mf«c v3 v3 v4 V V F v5 v6 v7 PM with geomorph v8

  11. Geomorph (2)

  12. Mesh Compression vspl(vs ,vl ,vr ,vs,vt,…) ’ ’ • Record deltas: • vt - vs • vs - vs • … vt ’ ’ vl vl vr vr vs ’ vs ’

  13. Selective Refinement vspl0 vspl1 vspli-1 vspln-1 M0

  14. Selective Refinement (2) • Rules for the vertex splits: • All involved vertices are present • doRefine(v) == TRUE  neighbours should be further refined • vertex is absent a previous vertex split was not executed, based on the two upper rules

  15. Selective Refinement (3) ViewFrustum Split not performed... ...because this split wasnot performed... ...which makes this vertex „not present“

  16. Selective Refinement (4) ViewFrustum if this would be present

  17. Construction Task: Construct Mn-1, Mn-2, ... M0 Naive Algorithm: { select random edge to collapse until resolution M0 faces }

  18. Construction (2) • Problems of naive algorithm: • Geometry is not preserved • Color, Normals etc. are not preserved • Discontinuities are not preserved

  19. Construction (3) • Better algorithm: • (Re-)Sample object • Simplify Object • Use energy function to measure accuracy • Extend to preserve... • surface geometry • color and normals • discontinuities

  20. Energy Function E(V)= Edist(V) + Espring(V) + Escalar(V)+Edisc(V) E negative  perform split (= less energy used for simplified mesh) furtherexplanations

  21. With better algorithm...

  22. PM have many advantages: lossless captures discrete attributes captures discontinuities continuous-resolution smooth LOD space-efficient progressive Summary

  23. Links (1) • Progressive Meshes [ Hoppe ] http://research.microsoft.com/~hoppe/(all images in this talk except those explicitly labeled courtesy of H. Hoppe)

  24. Links (2) • quadric error metric scheme [ Garland and Heckbert ] http://graphics.cs.uiuc.edu/~garland/papers.html • memoryless scheme [ Lindstrom and Turk ] http://www.cs.gatech.edu/gvu/people/Phd/Peter.Lindstrom.html

  25. Thank you for your attention ! Progressive Meshes Wallner and Wurzer

  26. Discussion Note • Problem of this approach: pictures courtesy of Markus Gross

  27. Discussion Note • Better Approach: picture courtesy of Markus Gross

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